5 citations · 14 across the 13 of their papers we have counts for
15 papers
Generalized Morrey-Campanato estimates for elliptic equations with coefficients of integrable oscillation
Laurent Seppecher
This work concerns regularity properties of weak solutions to elliptic equations in divergence form -div(au) = div F , under low regularity assumptions on both the coeffici…
Multi-parameter identification in systems of PDEs from internal data
Élie Bretin, Eliott Kacedan, Laurent Seppecher
This article aims to present a general analysis of a class of inverse problems that consists in recovering the elliptic parameter maps in systems of PDEs, such as the linear elasti…
Orthogonal modes of a fully anisotropic and heterogeneous elastic medium
Laurent Seppecher
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic ela…
Layer stripping approach to reconstruct shape defects in waveguides using locally resonant frequencies
Angèle Niclas, Laurent Seppecher
This article present a new method to reconstruct slowly varying width defects in 2D waveguides using one-side section measurements at locally resonant frequencies. At these frequen…
Lamb modes and Born approximation for small shape defects inversion in elastic plates
Eric Bonnetier, Angele Niclas, Laurent Seppecher
The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape def…
Reconstruction of smooth shape defects in waveguides using locally resonant frequencies
Angèle Niclas, Laurent Seppecher
This article aims to present a new method to reconstruct slowly varying width defects in 2D waveguides using locally resonant frequencies. At these frequencies, locally resonant mo…
The Helmholtz problem in slowly varying waveguides at locally resonant frequencies
Eric Bonnetier, Angèle Niclas, Laurent Seppecher +1
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phe…
Small defects reconstruction in waveguides from multifrequency one-side scattering data
Eric Bonnetier, Angèle Niclas, Laurent Seppecher +1
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work i…
Stability for finite element discretization of some elliptic inverse parameter problems from internal data -- application to elastography
Elie Bretin, Pierre Millien, Laurent Seppecher
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(μS) = \g f$ in a domain …
A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only
Habib Ammari, Elie Bretin, Pierre Millien +1
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a mediu…
Mathematical modeling in full-field optical coherence elastography
Habib Ammari, Elie Bretin, Pierre Millien +2
We provide a mathematical analysis of and a numerical framework for full-field optical coherence elastography, which has unique features including micron-scale resolution, real-tim…
Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation
Habib Ammari, Loc Hoang Nguyen, Laurent Seppecher
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded…
A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography
Habib Ammari, Pol Grasland-Mongrain, Pierre Millien +2
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magneti…
Radiative transfer and diffusion limits for wave field correlations in locally shifted random media
Habib Ammari, Emmanuel Bossy, Josselin Garnier +2
The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optica…
Reconstruction of a piecewise smooth absorption coefficient by an acousto-optic process
Habib Ammari, Josselin Garnier, Loc Hoang Nguyen +1
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstructi…